Xunzi's paradox is not a paradox that Xunzi discovered, but rather a paradox in Xunzi's writing on which others have commented on. It is perhaps not a paradox in the strictest sense of a logical paradox, but is a doctrine that seems to not be self-sustaining as such.
Xunzi was a philosopher of the Warring States period, and can be described in brief as a right wing Confucian. His students would go on to form the legalist school that would be the ideological basis of the Qin Dynasty, and would be responsible for burning Confucian books, along with Confucians. However, this was not directly the fault of Xunzi.
Xunzi believed, with Confucius, that rituals were needed to channel people's development. However, Xunzi did not believe in Mencius (who could be considered a "leftist" Confucian), who said that People are by nature good. Xunzi quite plainly stated "people are naturally corrupt".
Which brings us to the paradox: if people are naturally corrupt, where does their goodness come from? Mencius said the rituals were just the natural flowering of what was in an infant's heart. But Xunzi believed they had to be imposed from outside. Xunzi believed this happened in two ways: through the historical process when the Sage Kings trained the common people in the rituals of a civilized society; and through the non-historical process of mind taming people's nature.
The paradox is strengthened, however, by the addition of the mind. Where does this mind come from, if not from nature? It is not just that mind is a later abstraction of nature. Mencius, after all was well aware that the inborn good nature would need refinement across a person's lifespan, but Xunzi goes a step forward and declares that a third entity, mind, must be added, to explain the transformation from nature to ritual.
So, the question is just put off: where is this mind? Where does it come from? And if it is seperate from nature, how does it interact with nature to change it? Why add this third entity at all? And to explain the arising of mind from out of nowhere, do we need yet another entity? How far back can we go with this, once we have started to add entities to explain what seems to be a natural process?
This is not at all merely an issue of memorizing politics of ancient history. This view of Xunzi's that the mind is some abstraction removed from nature is very relevant to some modern issues in American culture, including racial politics and racial identity in American culture.
Put bluntly, there are plenty of people in America today who consider black people, and black street culture, to be "nature", and a rather bloody in tooth and claw nature at that. Sadly enough, not all of these people are white racists. There are plenty of people within the hip hop world who have taken the cry of keep it real to mean that any departure from the lowest common denominator to be a form of inauthenticity.
Where this relates back to Xunzi is that many people are critical of this type of LCD thinking follow some kind of belief in the scientifically, um, suspect doctrine of Evolutionary Psychology, where the lifestyles of our ancestors of millions of years ago give a descriptive, and perhaps prescriptive imperative for men to fight other men over scarce resources, and to use as many women sexually as they want. However, your typical middle class intellectual (hopefully) feels rather disgusted at the thought of human beings looking this way. But due to their "scientific" belief, they must deduce that the feelings of compassion in their minds are "unnatural", and that they are somehow "departing" from nature by feeling something other than the lowest common denominator. Thus they view themselves as being somehow "foreign" and "inauthentic", while the bogeyman of the rampaging black phallus, etc. is seen as the "natural" way that people would live, if not subjected to the power, mysteriously derived, of the outside "mind".
Yes, this is confusing. But that doesn't change the fact that this is, as clearly as it can be described, the basic structure of identity in America today.
And of course it is incorrect. It would be much simpler to stay with Mencius, and to remember that any construction of people as bloodthirsty and sexcrazy is just, that a construction, and is actually foreign to the human ear.